On conjugacy of unipotent elements in finite groups of Lie type

Let G be a connected reductive algebraic group defined over F-q, where q is a power of a prime p that is good for G. Let F be the Frobenius morphism associated with the F-q-structure on G and set G = G(F), the fixed point subgroup of F. Let P be an F-stable parabolic subgroup of G and let U be the unipotent radical of P; set P = P-F and U = U-F. Let G(uni) be the set of unipotent elements in G. In this note we show that the number of conjugacy classes of U in G(uni) is given by a polynomial in q with integer coefficients.